You prepare to take a vacation visiting Buenos Aires, Argentina, after Term $3$ is over. Let us consider the following $($simplified$)$ process for airline food tray preparation for your flight to Buenos Aires.

The process consists of three steps. In the first step, each tray is loaded with a packaged snack, a container with fruit, and a packet with plastic utensils. This activity requires $1\mathrm{.}2$ minutes per tray. In Step $2,$ trays are shrink$-$wrapped in batches using a machine that requires a setup of $10$ minutes for each batch of $30$ trays. After the setup, it takes $1$ minute to shrink$-$wrap each tray in the batch. Finally, the last step is to place the trays in airplane food carts. In this step, each tray requires $1$ minute of processing $($i$.$e$.,$ it takes $1$ minute to place one tray in the cart$).$ The capacity of each cart is of $28$ food$-$trays. After filling a cart, it takes an average of $7$ minutes to transport the filled cart to the loading truck and setup another empty cart for placing a new set of trays.